Chapter 23 Latent variable models in econometrics

This chapter discusses latent variable models in econometrics. The essential characteristic of a latent variable is revealed by the fact that the system of linear structural equations in which it appears cannot be manipulated so as to express the variable as a function of measured variables only. It discusses that for a linear structural equation system to be called latent variable model, there is at least one more independent variable than the number of measured variables. Usage of the term independent variable as contrasted with exogenous variable, the more common phrase in econometrics, includes measurement errors and the equation residuals themselves. In the functional model, the true values of exogenous variables are fixed variates, and therefore, are best thought of as nuisance parameters that may have to be estimated en route to getting consistent estimates of the primary structural parameters of interest. Finally, restrictions on a model's covariance structure, which are commonplace in sociometric and psychometric modeling, also serve to aid identification.